Over the last several years, wireless networks have become indispensable tools for carrying voice and data communications for both business and personal use. Wireless networks partition a given geographical region into cells. Each cell is given a base station that serves as the anchor point to the network for all users in the cell. Users are assigned to the different cells based on, for example, channel conditions and network loading.
In current networks, coordination between base stations is not considered; users are only controlled by their assigned base station. However, due to the nature of wireless transmission, users in neighboring cells interfere with the transmission in a given cell. In general, this out-of-cell interference is unknown and uncontrollable. Unfortunately, the performance of the channels in the cell critically depends on the out-of-cell interference since the achievable transmission rate of each channel is related to its signal-to-interference-plus-noise ratio experienced at the receiver.
The network is then faced with the task of determining its maximum average rate of reliable transmission under the uncertainty on the interference level. Cover, in “Broadcast Channels,” IEEE Transactions on Information Theory, vol. IT-18, pp. 2-14, January 1972 (incorporated herein by reference), defined such compound channels and showed their equivalence to broadcast channels. Cover proposed and analyzed a solution, which he called “superposition coding,” for reliable transmission over such channels. In particular, Cover showed that superposition coding achieves larger throughput than time-sharing techniques.
Subsequently, Bergmans, in “A Simple Converse for Broadcast Channels with Additive White Gaussian Noise Maximum Likelihood Decoding,” IEEE Transactions on Information Theory, vol. IT-20, pp. 279-280, March 1974 (incorporated herein by reference), demonstrated the optimality of superposition coding. The main idea behind superposition coding, as it pertains to channel throughput, is to make sure that some data is correctly received even when the interference is large; additional information can be received when the interference is small.
Shamai, in “A Broadcast Strategy for the Gaussian Slowly Fading Channel,” in Proceedings of the IEEE International Symposium on Information Theory 1997, p. 150 (incorporated herein by reference), calculates the maximum throughput achievable under superposition coding, but shows that achieving the maximum throughput requires an infinite number of coding levels. Liu, et al., in “Optimal Rate Allocation for Superposition Coding in Quasi-static Fading Channels,” in Proceedings of IEEE International Symposium on Information Theory 2002, p. 111 (incorporated herein by reference), consider only a finite number of levels in the superposition coding and show that the performance achieved with two levels is fairly close to the maximum throughput. However, Liu, et al., assume that the transmitter does not have any information on the state of the channel. On the other hand, Whiting, et al., in “Optimal Encoding over Uncertain Channels with Decoding Delay Constraints,” in Proceedings of the IEEE International Symposium on Information Theory 2000, p. 430 (incorporated herein by reference), assume the transmitter to have delayed feedback knowledge about the channel state and a finite decoding delay. Whiting, et al., then provide the maximum achievable average rate using a broadcast approach.
All of the above-referenced prior art approaches have assumed that the transmission rates are of infinite granularity. However, in practical scenarios (due to standard specifications, practical implementations and the cost of building commercial transmitters and receivers), the set of allowed transmission rates is finite and predetermined, and the transmitters are constrained to only use some of these specified rates.
What is needed in the art is a technique for determining the throughput achievable under superposition coding given a finite, predetermined set of allowed transmission rates. What is further needed in the art is a system and a method for performing such technique.